导出方程

The non_singular fictitious boundary integral equations are derived by using the fundamental solutions and the singular points exterior to domain techniques.

利用基本解和域外奇点技术导出了弹性力学平面问题的非奇异虚边界积分方程，然后利用虚边界元－边界子段法对导出的积分方程进行数值求解。

Geostatics and hydrokinetics are used to develop equations relating the variation of the mass, centroid and moment of inertia because of the fuel combustion, and the change of the propeller thrust as the AUV cruises. A complete mathematical model is presented for an AUV with variable mass and velocity.

利用刚体分析动力学和理论流体力学的基本理论，研究水下自航器因燃料的消耗而引起的质量变化、质心位置和转动惯量的变化，导出描述其变化规律的方程；研究因推力变化而引起速度的改变，导出推力变化方程。

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

The diffusion wave equation with the neglect of lateral discharge and backwater effect is resolved, and the analytical solution is represented by S-curve or duration unit hydrograph.

导出了具有分布式旁流的自由下边界条件的扩散波方程的解析解，这是对前人导出的不考虑旁流的自由下边界条件的扩散波方程解析解的补充。

Then, the equation was changed into the standard form of the Mathieu equation using Galerkin method.

首先在载流薄板的磁弹性非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板在电磁场与机械荷载共同作用下的磁弹性动力稳定方程，然后应用Galerkin方法将稳定方程整理为Mathieu方程的标准形式，并将薄板的动力稳定性问题归结为对Mathieu方程的求解。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究： 1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值模式； 2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程； 3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布； 4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式； 5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分析。

According to the neural cable model, this dissertation deduced a stable solution. Based on the lead model, the vibratory equation of electriferous lead in a static magnetic field is set up under the condition of coupling magneto-acoustic field. It is verified that the vibration in bio-tissue is proportional to with the product of the magnitude of the magnetic field, the current amplitude and the sinusoid of angle between them.

根据神经的电缆模型，论文导出直流稳态解；基于导线模型，根据洛仑兹方程和细弦上的波动方程，论文建立了磁声耦合条件下带电导线在磁场中的振动方程，导出生物组织中的振动与磁场的大小、电流的大小和磁场与电流角度的正弦值乘积成正比。

It also derives calculation formulas of various dispersed coefficient to set up three-dimensional turbulence model of draft tube and confirm the solving method.

对流场控制方程及三维湍流模型进行了深入的分析与研究，导出了通用微分方程，用有限体积法推导了通用微分方程的离散形式，并导出了各种离散系数的计算公式，建立了尾水管的三维湍流模型，并确定了求解方法。

We can lead out the equivalent border integral equation by Green the second equation,dividing the inner border in the liquid into a series strip of awls shell or cylindrical shell ,and solve border integral equation along different segment of border, then lead out border integral equation.

由Green第二恒等式导出等价的边界积分方程，将液体内边界分成一系列锥壳或柱壳状条，对边界积分方程进行分段积分，导出边界元格式方程。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。